We show that for every connected graph G of diameter 3, the graph G3 has average degree 7 4 (G). We also provide an example showing that this bound is best possible. This resolv...
The vertex set of a halved cube Qd consists of a bipartition vertex set of a cube Qd and two vertices are adjacent if they have a common neighbour in the cube. Let d ≥ 5. Then i...
Acyclic cubical complexes have first been introduced by Bandelt and Chepoi in analogy to acyclic simplicial complexes. They characterized them by cube contraction and elimination ...
A hierarchy of classes of graphs is proposed which includes hypercubes, acyclic cubical complexes, median graphs, almost median graphs, premedian graphs and partial cubes. Structu...
For a given connected graph G of order n, a routing R in G is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forw...